Just to make sure, did you check the fonts in the Appearance → Custom Design → Fonts panel and not find anything that will do? If you had a specific font in mind, let me know the font name and why you picked it and I'll pass along that feedback to our developers.

We had already tried all steps suggested by you, but nothing was changed.

It sounds like your Typekit kit was not setup correctly. I can try to help you verify the setup.

First, double check that your Typekit Kit ID is correct on this page:
https://mipiacemancheno.wordpress.com/wp-admin/themes.php?page=custom-fonts

Next, make sure your domain is entered correctly in your Typekit Kit on the http://typekit.com/ site. Here is an example: http://cl.ly/OyLW

After any changes are made on the http://typekit.com/ side, you must click the Publish button and then wait a few minutes for the change to take effect. Here is what my Typekit Kit looks like: http://cl.ly/Ox7I

Last, your selectors must be setup correctly. There are two ways to do it, one is to add the selectors for the elements you want to change right into the Typekit Kit. Example: http://cl.ly/Owyc

The other way is to add the font using CSS on the WordPress.com side. You have to use the font names specified by Typekit or it won't work. In your Typekit Kit, click the "Using fonts in CSS" link to see how to do it. Here is an example for the Daniel font: http://cl.ly/OyAz

If you're still having trouble after checking the setup one more time, please let me know.

I bought Custom Design and I register to Typekit so I really don't know what doesn't work with font upload.

Are you referring to the http://mipiacemancheno.com/ site? That site is currently using the WordPress.com Custom Fonts feature which lets you select from 50+ selected fonts that are served by Typekit. In order to use fonts other than the selected ones seen on the Appearance → Custom Design → Fonts page in your blog dashboard, you would have needed to setup a separate Typekit account, setup a kit for your domain through their site, made sure the fonts you wanted to use were selected in the kit on the typekit.com side, and also connected your Typekit account to your WordPress.com using the advanced fonts mode. Your site is not actually setup to use the advanced mode right now, but is that what you had setup before? Here are the instructions you would have needed to follow:
http://en.support.wordpress.com/custom-design/custom-fonts/#advanced-mode

The strange think and we are 2 administrators and both of us are able to see the different font, but other visitors are not....really strange.

This could happen if you and the other administrator have the font installed locally.

What I have learned is that you can use Firebug to look at your blog and identify the code for certain sections. You do however still need some CSS programming skills to be able to identify the right Selectors.

If you can identify the right Selectors you can put them directly into TypeKit Editor to apply across your site or you can write some over riding code in CSS editor for certain sections of your site.

Please correct me if I'm wrong thesacredpath. And thanks for the help!

.entry-title, .entry-title a {
    font-style: normal;
}

Timethief - it helps a bit but still leaves me with having to enter CSS code.
I want to simply enter the selectors in the typekit editor and not mess with too many things, before they break. So I would like to identify the selectors. As a second option I'll study CSS coding (one day...).

thesacredpath - I selected two fonts in TypeKit. One for body of posts and the other for all the rest (h1 - h6 and site header and subtitle, menu, etc...)
That is a lot of Selectors, right?

Otherwise, if I can just make the headers of my posts to NOT be italic, it will make me feel a lot better. Can you give me the CSS code for that?
How do I make sure it overrides what is there already?

I did "Publish" and I did put the TypeKit number in on WordPress.com's side and it says it is all fine.

Can someone not just give me a list of the selectors I need to put in? I just want my selected fonts to pull through to my site without going and writing CSS code in WordPress.

font-family: "Daniel", serif;

font-family: "lint-mccree", sans-serif;

Besides using fonts that are installed on the viewer's computer, it is possible to install fonts on a web server so they will work for all visitors. To use a font, you need to make sure you have the proper licensing. At WordPress.com, we use a font service called Typekit to serve custom fonts, and those are included in our Custom Design upgrade which you can find out more about here:
https://store.wordpress.com/premium-upgrades/custom-design/

Custom fonts can be set using the Appearance → Themes → Customize → Fonts panel. Also, anyone can try them before purchasing by going to Appearance → Themes → Customize → Custom Design and clicking the "Try Now" button.

To find out more about font stacks in general, see http://unitinteractive.com/blog/2008/06/26/better-css-font-stacks/

#header {
margin: 0;
background: url('http://mipiacemancheno.files.wordpress.com/2013/05/titolo.png') center no-repeat;
padding: 0;
height: 260px;
width: 1054px;
color: #000;
}

h1 {
display: none;
}

h2, h2 a, h2 a:visited, h3, h3 a, h3 a:visited {
font-family: "lint-mccree", sans-serif;
font-size: 1.8em;
font-weight: 900;
}

p {
font-family: "Daniel", serif;
font-size: 1.8em;
font-weight: bold;
line-height: 1.5em;
}

#sidebar, #sidebar h2, #wp-calendar caption, cite {
font-family: "lint-mccree", sans-serif;
font-size: 1.2em;

(2) Changing font colors in text in posts or pages either post by post or page by page using the #4 icon (Select text color – change the text color) in Row 2 the Visual editor. http://en.support.wordpress.com/visual-editor/#row-2

(3) Changing all font families, colors and sizes throughout the whole blog by purchasing an annually renewable Custom Design upgrade and using Typekit Fonts with Staff support. http://en.support.wordpress.com/custom-design/

h2#description {
font-family: ronnia-1,ronnia-2,Merriweather,serif !important;
font-size: 12px;
}

Thank you very much for your help in advance.

.main-navigation a:link {
text-transform: uppercase;
}

.main-navigation a:hover {
text-transform: uppercase;
}